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400 Digits of Pi

Published on Friday, October 08, 2010 in , ,

Memorizing Pi to 400 Decimal Places

The obvious first question is, “What exactly IS pi to 400 decimal places?” Here it is:
Pi=3.1415926535897932384626433832795028841971
        6939937510582097494459230781640628620899
        8628034825342117067982148086513282306647
        0938446095505822317253594081284811174502
        8410270193852110555964462294895493038196
        4428810975665933446128475648233786783165
        2712019091456485669234603486104543266482
        1339360726024914127372458700660631558817
        4881520920962829254091715364367892590360
        0113305305488204665213841469519415116094
There are many different ways to memorize pi. There are even those “pi purists” who refuse to use the mnemonic alphabet, and attempt to learn the numbers as numbers themselves. University of Edinburgh professor Alexander Craig Aitken learned it to a particular rhythm. Others assign meaning directly to the numbers themselves. For example look at the last four numbers in the first row above (1971). Some might remember this number as the year they were born or that some other memorable event from that year.

Are these methods effective? They certainly seem to be for the individuals who create them. It can be tricky though, for others to try and learn these methods, especially as the associations are often highly personal.


What advantages does this method offer? First, it can be taught to anyone who is familiar with both the mnemonic alphabet and the English language (indeed, it can be easily adapted to almost any Germanic language). Second, it doesn't just teach the digits in order, but out of order at the same time! What do I mean by out of order?

Imagine not just knowing the digits of pi themselves, but also where they are relative to each other. You could face challenges like these:
* Given the proper location, you can recall a corresponding group of four digits.
* Recall a single digit in the Nth position after the decimal point
* Given a group of four numbers, you can recall the location
* You can even recall entire sequences of numbers from pi
The traditional mnemonic alphabet method for pi is based on converting the numbers into words, and then linking them into a story. As you can see, if you forget just one element of the story, the entire number is thrown off! The method taught here eliminates the story aspect, and makes the memorization both simpler AND much more effective at the same time!

Prerequisites:

Link System
Major System

When you're ready, click to continue.

Pi Chart

To make this easier, we'll break the 400 digits after the decimal point (note that the initial 3 isn't in the chart itself) into a 10x10 grid of four digit numbers:

Pi=3......
 12345678910
A1415926535897932384626433832795028841971
B6939937510582097494459230781640628620899
C8628034825342117067982148086513282306647
D0938446095505822317253594081284811174502
E8410270193852110555964462294895493038196
F4428810975665933446128475648233786783165
G2712019091456485669234603486104543266482
H1339360726024914127372458700660631558817
I4881520920962829254091715364367892590360
J0113305305488204665213841469519415116094

Now, we'll turn each set of coordinates and each four-digit number into words we can associate with each other. For example, since 1 is equal to a “t” sound, then we can make A1 represent the word “ATe”. The number at that point in the grid, 1415, translates into the sounds of t, r, t, and l - so we'll represent that number with the word “TuRTLe”. Now, you link the word “ATe” to the word “TuRTLe” in a humorous or exaggerated way. Picturing yourself just having ate a turtle should do it. In a similar manner, you can turn A2 into “ANnoy” and 9265 into “PuNCH Low”, and picture yourself being annoyed by a punch low on your body, perhaps by a disembodied fist (just to make the picture unusual and memorable).

Below is a complete list of associations. Go through each one and associate the words together in silly ways. The more memorable the image, the stronger a memory key it will be! Assuming you already know what sounds go with what number in the Peg system, you should have little trouble remembering the entire chart in a short time!

You can also find alternate mnemonics, courtesy of Train Your Brain and Entertain user Wallace Gluck, in my New Pi Mnemonics post.

Once you've made each of the associations, go to the next section to learn various ways to present this feat. If you'd rather be tested right away, practice with the 400-digit Pi quiz!

MnemonicsMnemonics
A1: ATe - TuRTLeB1: BaD - SHaBBy MoB
A2: ANnoy - PuNCH LowB2: BoNe - PuMa CLaw
A3: AiM - MaLe FiBB3: BuM - weT SaLiVa
A4: AiR - KeeP MooN!B4: BeeR - NoSe PiCK
A5: ALe - Mmmmm...FReSH!B5: BeLL - RePaiReR
A6: ASH - New GeRMB6: BaDGe - Law, By NaMe
A7: ACHe - MoVe hiM? No!B7: BaG - SaCK FooD
A8: A Vow - CouPLeSB8: BuFF - CHaiR'S waSH
A9: (h)APPy - iN FaVorB9: BiB - NePHew CHiN
A10: ACe - ToP CaTB10: BuS - SaVe BoB!
  
C1: CaT - FiSH kNiFeD1: DoT - SoaP 'eM oFF
C2: CaN - SMuRFD2: DeN - aiR RuSHeS
C3: CoMa - aNNuL MaRRyD3: DaMn - PoLo LoSS
C4: CaR - huNT DoGD4: DRy - LV NeoN
C5: CoaL - iCe aGe CuBeD5: DeaL - MaDe GaiN
C6: CaSH - FiNDeRD6: DaSH - LiMb LeaP
C7: CooK - haVe hiS FuDGeD7: DoG - ReCeiVeD
C8: CaVe - LouD MaND8: DiVe - NaVy aRRiVe
C9: CuP - VeNoMSD9: DoPe - iDea iDioTiC
C10: CaSe - JuDGe woRKD10: DiCe - RoLL SooN
  
E1: EDDy - FjoRDSF1: FighT - waRRioR kNiFe
E2: EN - eNCaSeDF2: FuN - FaT SPy
E3: EM - BeaM FeLLF3: FoaM - CoLLeGe waSH
E4: ERR - eNTiTieSF4: FeaR - heLP! MoMMy!
E5: EEL - Lay Low heLPF5: FiLe - ReRuSHeD
E6: EDGe - SHeaR RiDGeF6: FiSH - New FoRK
E7: EGG - New NeighBoRF7: FaKe - Lie, SHeRiFF?
E8: EVe - ViP LuReF8: FiFe - eNeMy MoCK
E9: EBB - Bay MuSeuMF9: FiB - FiSH GooF
E10: EaSy - PHoTo PaGeF10: FaCe - MeeT JuLie
  
G1: GuT - NiCoTiNeH1: HaTe - DooM MoB
G2: GowN - STePSH2: HeN - Ma haTCHeS eGG
G3: GaMe - PaTRoLH3: HoMe - eNJoy SuN
G4: GeaR - SHRiVeLH4: HaRe - RaBBiT eaR
G5: GoaL - eaCH CHiP iNH5: HeLLo - aDD iNCoMe
G6: GuSH - eMeRGeSH6: HeDGE - CoiN RoLe
G7: GaG - MoRe FiSHH7: HoG - haVe eXCeSS
G8: GaFF - DiCe ReaL?H8: HaVe - JuDGe'S iSSue
G9: GaP - Re-MaNaGeH9: HiP - MeTaL aLLoy
G10: GaS - SHaRe VaNH10: HoSe - halF-oFF TaG
  
I1: IT - ReViVe iTJ1: JeT - STaDiuM
I2: INN - LoNe SPaJ2: JoiN - MoSLeM
I3: I'M - NoiSy, BiTCHyJ3: JaM - haS LaRVa
I4: IRe - eNouGH! uNhaPPy!J4: JeeR - oFteN SouR
I5: ILL - iNhaLeRSJ5: JaiL - huGe JaiL Now
I6: ItCH - PeT CaTJ6: JuDGe - DeeM FaiR
I7: IKe - Law MaJoRJ7: JacK - TiRe SHoP
I8: IVy - MaGiC iVyJ8: JaVa - OlD BRew
I9: (y)IPe - PaiN yeLPJ9: JoB - DeLeTeD
I10: ICe - SMaSHeSJ10: JaS - JaSPeR

Presenting Your Knowledge of Pi

The best way to be ready to demonstrate this feat is to create a small chart you can carry around in your wallet. Create a small ID-card sized chart, including the coordinates (A-J & 1-10), on your printer and have it laminated. You are now ready to be quizzed in a variety of ways.

Basic 4-Digits

If you've made the associations properly, you can already do this one! Simply have someone name a set of coordinates, and recall the correct number via the mnemonic association.

Intermediate 4-Digits

Ask for a set of coordinates, and mention you'll give the number backwards! When you recall the mnemonic word, simply convert them into numbers starting with the rightmost (last) digit, and continuing through to the leftmost (first) digit. This gets easier with practice. To those watching, though, this seems MUCH tougher than it actually is.

Advanced 4-Digits

In this version, you ask for a set of four digits, and you recall the coordinates at which they are located. This will take a little practice, as you have to be able to quickly translate a given number into it's mnemonic association, and then recall the coordinate mnemonic. It's a startling addition to your pi feat, though.

Nth Digit of Pi

This will require some mental calculations. Have someone name any position up to 400 digits after the decimal place. Let's say they ask for the 157th digit after the decimal place. You first divide by 4, and remember not only the number but the remainder. In our example, this would be 39 with a remainder of 1 (157 / 4 = 39 r 1). The “3” in the “39” tells us to skip 3 complete rows (A, B & C) and look for it in the next row (row D). The “9” in the “39” tells us how many complete columns over the number is. We already know we're looking for D9. In our example, we have a remainder of 1, so we now know we're looking for the 1st digit after D9. In other words, we're looking for the first digit of D10. We know D10 is “DiCe” which is associated with “RoLL SooN”. “R” is the first letter of the associated phrase, so we can state that 4 is the 157th digit after the decimal place!

Rows, Columns and Diagonals

This is impressive enough to use as a finale, but not much more difficult than the “Basic 4-Digits” feat above. You simply ask for any row (A-J) and recite it starting with the 1st set of four digits, and continuing through with the 10th set of four digits in that row. Columns can be called instead, and you just start with the A coordinates for that column, and continue through to the J coordinates. You can even have them ask for diagonals, either A1 through J10 or A10 through J1. With a little extra practice, you can run through every row, column or diagonal backwards!

Practice now with the pi quiz!

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